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Graphs, groups and pseudo-similar vertices

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

W. L. Kocay
W. L. Kocay
Affiliation:
Department of Computer Science University of QueenslandSt. Lucia, Queensland, Australia Department of Computer Science University of ManitobaWinnipeg, ManitobaCanadaR3T 2N2
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Abstract

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Vertices u0, u1, …, uk−1 of a graph X are mutually pseudo-similar if X − u0 ≌ X − u1 ≌ … ≌ X − uk−1, but no two of the vertices are related by an automorphism of X. We describe a method for constructing graphs with a set of k≥2 mutually pseudo-similar vertices, using a group with a special subgroup. We show that in all graphs with pseudo-similar vertices, the vertices are pseudo-similar due to the action of a group on the cosets of some subgroup.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 181 - 189
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Bollobas, B., Graph theory (Springer-Verlag, New York, 1979).CrossRefGoogle Scholar
[2]Bondy, J. A. and Murty, U. S. R., Graph theory with applications (Macmillan, London, 1976).CrossRefGoogle Scholar
[3]Godsil, C. D., Graphs with regular groups (Ph.D. Thesis, University of Melbourne, 1979).Google Scholar
[4]Godsil, C. D. and Kocay, W. L., ‘Constructing graphs with pairs of pseudo-similar vertices’, J. Combinatorial Theory Ser. B, to appear.Google Scholar
[5]Godsil, C. D. and Kocay, W. L., ‘Graphs with 3 mutually pseudo-similar vertices’, submitted for publication.Google Scholar
[6]Harary, F. and Palmer, E., ‘On similar points of a graph’, J. Math. Mech. 15 (1966), 623–630.Google Scholar
[7]Imrich, W., ‘Subgroup theorems and graphs’, Combinatorial mathematics V, (Springer-Verlag, New York, 1977).Google Scholar
[8]Johnson, D. M., Topics in the theory of group presentations (Cambridge University Press, 1980).CrossRefGoogle Scholar
[9]Kimble, R., Stockmeyer, P. and Schwenk, A., ‘Pseudosimilar vertices in a graph’, J. Graph Theory 5 (1981), 171–181.CrossRefGoogle Scholar
[10]Kocay, W. L., ‘On pseudo-similar vertices’, Ars Combinatoria 10 (1980), 147–163.Google Scholar
[11]Kocay, W. L., ‘Some new methods in reconstruction theory’, Proceedings of the Ninth Australian Combinatorial Conference (Springer, to appear).Google Scholar
[12]Kocay, W. L., ‘A small graph with three mutually pseudo-similar vertices’, in preparation.Google Scholar
[13]Kocay, W. L, ‘An enumeration of coset diagrams for pseudo-similar vertices’, in preparation.Google Scholar
[14]Krishnamoorthy, V. and Parthasarathy, S., ‘Cospectral graphs and digraphs with given automorphism group’, J. Combinatorial Theory Ser. B 19 (1975), 204–213.CrossRefGoogle Scholar